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            <h1>අසම්පූර්ණතොරතුරු සහිත ක්රීඩා වල අවම කිරීම කනගාටු කරන්න (CFR)</h1>
<p>කඩදාසි <a href="http://martin.zinkevich.org/publications/regretpoker.pdf">කනගාටුව අසම්පූර්ණ තොරතුරු සහිත ක්රීඩා වල අවම කිරීම</a> ප්රතිවිරුද්ධ කනගාටුව හඳුන්වා දෙන අතර ස්වයං නාට්යය තුළින් ප්රතිවිරුද්ධ කනගාටුව අවම කිරීම නැෂ් සමතුලිතතාවයට ළඟා වීමට භාවිතා කළ හැකි ආකාරය. ඇල්ගොරිතම හැඳින්වෙන්නේ ප්රතිවිරුද්ධ කනගාටුව අවම කිරීම (<strong>CFR</strong>) ලෙසිනි. </p>
<p><a href="http://mlanctot.info/files/papers/nips09mccfr.pdf">පුළුල් ක්රීඩා වල කනගාටුව අවම කිරීම සඳහා මොන්ටේ කාලෝ නියැදීම</a> කඩදාසි මොන්ටේ කාලෝ ප්රතිවිරුද්ධ කනගාටුව අවම කිරීම (<strong>MCCFR</strong>) හඳුන්වා දෙයි, එහිදී අපි ක්රීඩා ගසෙන් සාම්පල ලබාගෙන කනගාටුව තක්සේරු කරමු. </p>
<p>අපගේපයිතන් ක්රියාත්මක කිරීම නිබන්ධනයක් මෙන් පහසුවෙන් තේරුම් ගැනීමට අපි උත්සාහ කළෙමු. අපි එය <a href="kuhn/index.html">ඉතා සරල අසම්පූර්ණ තොරතුරු ක්රීඩාවක් මත ධාවනය කරමු Kuhn පෝකර් ගහන්න දන්නවානම්</a>. </p>
<p><a href="https://colab.research.google.com/github/labmlai/annotated_deep_learning_paper_implementations/blob/master/labml_nn/cfr/kuhn/experiment.ipynb"><img alt="Open In Colab" src="https://colab.research.google.com/assets/colab-badge.svg"></a></p>
<p><a href="https://twitter.com/labmlai/status/1407186002255380484"><img alt="Twitter thread" src="https://img.shields.io/twitter/url?style=social&url=https%3A%2F%2Ftwitter.com%2Flabmlai%2Fstatus%2F1407186002255380484"></a> ට්විටර් නූල්</p>
<h2>හැඳින්වීම</h2>
<p>අපිඅහම්බෙන් නියැදීම් (CS) සමඟ මොන්ටේ කාලෝ ප්රතිවිරුද්ධ කනගාටුව අවම කිරීම (MCCFR) ක්රියාත්මක කරමු. එය iteratively, සියලු ක්රීඩකයා ක්රියා උත්සාහ ක්රීඩාව ගස කොටසක් ගවේෂණය, නමුත් අවස්ථාවක් සිදුවීම් නියැදීම්. අවස්ථාවක් සිදුවීම් කාඩ්පත් ගනුදෙනු වැනි දේවල් ය; ඔවුන් නැවත එක් වරක් sampled තබා ඇත. එවිට එය ගණනය කරන්නේ, එක් එක් ක්රියාව සඳහා, එම පියවර ගැනීම වෙනුවට වර්තමාන උපායමාර්ගය අනුගමනය කිරීමේ <em>කනගාටුව</em> . ඉන්පසු එය කනගාටුව ගැලපීම භාවිතා කරමින් ඊළඟ පුනරාවර්තනය සඳහා මෙම කනගාටු මත පදනම් වූ උපාය යාවත්කාලීන කරයි. අවසාන වශයෙන්, එය පුනරාවර්තන පුරා උපාය මාර්ගවල සාමාන්යය ගණනය කරයි, එය අප ප්රමාණවත් පුනරාවර්තන දිව ගියහොත් නැෂ් සමතුලිතතාවයට ඉතා සමීප වේ. </p>
<p>අපිමුලින්ම ගණිතමය අංකනය සහ න්යාය හඳුන්වා දෙන්නෙමු. </p>
<h3>ක්රීඩකයා</h3>
<p>ක්රීඩකයෙක්විසින් දැක්වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.72243em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdn" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqen" style="">i</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeg" style="margin-right:0.10903em">N</span></span></span></span></span></span></span>, ක්රීඩකයන් සමූහයක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqeg" style=""><span class="mord mathnormal" style="margin-right:0.10903em">N</span></span></span></span></span></span> කොහෙද. </p>
<h3><a href="#History">ඉතිහාසය</a></h3>
<p>ඉතිහාසය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdk" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqee" style="margin-right:0.08125em">H</span></span></span></span></span></span></span> යනු ඇතුළු ක්රියා වල අනුක්රමයකි අවස්ථාවක් සිදුවීම්, <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqee" style=""><span class="mord mathnormal" style="margin-right:0.08125em">H</span></span></span></span></span></span> එය සියලු ඉතිහාසයන්ගේ සමූහයයි. </p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8193em;vertical-align:-0.13597em;"></span><span class="mord coloredeq eqej" style=""><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">⊆</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqee" style=""><span class="mord mathnormal" style="margin-right:0.08125em">H</span></span></span></span></span></span> යනු පර්යන්ත ඉතිහාස සමූහයයි (ක්රීඩාව අවසන්). </p>
<h3>ක්රියාව</h3>
<p>ක්රියාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span></span></span></span></span>, පර්යන්ත <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdk" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqee" style="margin-right:0.08125em">H</span></span></span></span></span></span></span> නොවන <a href="#History">ඉතිහාසයක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqce" style=""><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel" style="">:</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqee" style="margin-right:0.08125em">H</span></span></span></span></span></span></span></span> </a>කොහේද? </p>
<h3><a href="#InfoSet">තොරතුරු කට්ටලය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdy" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></a></h3>
<p>ක්රීඩකයා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdy" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqct" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqcw" style=""><span class="mord mathcal coloredeq eqef" style="margin-right:0.07382em">I</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> සඳහා<strong>සකසා ඇති තොරතුරු</strong> ඉතිහාසයකට සමාන <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> වන <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdk" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqee" style="margin-right:0.08125em">H</span></span></span></span></span></span></span> නමුත් ක්රීඩකයාට පෙනෙන ක්රියාවන් පමණක් අඩංගු වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>. එනම්, ඉතිහාසයේ ප්රතිවිරුද්ධ ක්රීඩකයාට ගනුදෙනු <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span> කරන කාඩ්පත් වැනි ක්රියාවන්/සිදුවීම් අඩංගු වන අතර ඒවා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdy" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> නොලැබෙනු ඇත. </p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqct" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqcw" style=""><span class="mord mathcal coloredeq eqef" style="margin-right:0.07382em">I</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> ක්රීඩකයාගේ <strong>තොරතුරු කොටස</strong> ලෙස හැඳින්වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>. </p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdl" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span></span></span></span></span></span> යනු ලබා දී ඇති තොරතුරු කට්ටලයකට අයත් සියලු ඉතිහාස සමූහයයි; එනම් එම සියලු ඉතිහාසයන් ක්රීඩකයාගේ ඇසට සමාන වේ. </p>
<p><a id="Strategy"></a></p>
<h3>උපායමාර්ගය</h3>
<p><strong>ක්රීඩකයාගේඋපාය මාර්ගය</strong> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>, ක්රියාවන්ට වඩා බෙදා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.6891em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdg" style=""><span class="mord" style=""><span class="mord" style="">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> හැරීමකි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdo" style=""><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqdy" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span>, ක්රීඩකයා සඳහා සියලු උපාය මාර්ග සමූහයක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdg" style=""><span class="mord" style=""><span class="mord" style="">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> කොහේද <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord coloredeq eqep" style=""><span class="mord mathnormal" style="">t</span></span></span></span></span></span>-th පුනරාවර්තනය පිළිබඳ උපාය මාර්ග මගින් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.943556em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqda" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>දැක්වේ. </p>
<p>මූලෝපායඅර්ථ දක්වා ඇත්තේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span></span></span></span></span> දී ඇති තොරතුරු කට්ටලයක් සඳහා ක්රියාමාර්ගයක් ගැනීමේ සම්භාවිතාවක් ලෙස ය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span></span></span>,</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mopen">(</span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span></span></span></span></p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span></span></span></span> සියලුම ක්රීඩකයන්ගේ <strong>උපාය මාර්ග වලින් සමන්විත උපාය මාර්ග පැතිකඩයි</strong> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span></span></span></span></span></p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqcx" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span></span></span> හැර සියලුම ක්රීඩකයන්ගේ උපාය මාර්ග වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><a id="HistoryProbability"></a></p>
<h3>ඉතිහාසයේසම්භාවිතාව</h3>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqcu" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span> උපාය මාර්ග පැතිකඩ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span> සමඟ ඉතිහාසය කරා ළඟා වීමේ සම්භාවිතාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span></span></span></span>වේ. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.108031em;vertical-align:-0.358031em;"></span><span class="mord coloredeq eqcm" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqcu" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen coloredeq eqcu" style="">(</span><span class="mord coloredeq eqcu" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose coloredeq eqcu" style="">)</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.161964em;"><span style="top:-2.4003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.358031em;"><span></span></span></span></span></span></span></span></span></span></span></span> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>ක්රීඩකයාගේ දායකත්වය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span> නොමැතිව ළඟා වීමේ සම්භාවිතාව; එනම් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> ක්රීඩකයා අනුගමනය කළ යුතු ක්රියාමාර්ග <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span> සම්භාවිතාවක් සමඟ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqed" style=""><span class="mord" style="">1</span></span></span></span></span></span>. </p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0497em;vertical-align:-0.29969999999999997em;"></span><span class="mord coloredeq eqco" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqcu" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen coloredeq eqcu" style="">(</span><span class="mord coloredeq eqcu" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose coloredeq eqcu" style="">)</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.161964em;"><span style="top:-2.4003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29969999999999997em;"><span></span></span></span></span></span></span></span></span></span></span></span> පමණක් ක්රීඩකයා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>දායකත්වය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span> සමග ළඟා වීමේ සම්භාවිතාව වේ. එනම්, <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqcu" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.108031em;vertical-align:-0.358031em;"></span><span class="mord coloredeq eqco" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqcu" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen coloredeq eqcu" style="">(</span><span class="mord coloredeq eqcu" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose coloredeq eqcu" style="">)</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.161964em;"><span style="top:-2.4003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29969999999999997em;"><span></span></span></span></span></span></span></span><span class="mord coloredeq eqcm" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqcu" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen coloredeq eqcu" style="">(</span><span class="mord coloredeq eqcu" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose coloredeq eqcu" style="">)</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.161964em;"><span style="top:-2.4003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.358031em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p>තොරතුරුකට්ටලයක් වෙත ළඟා වීමේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span></span></span> සම්භාවිතාව, <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqdp" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.3794880000000003em;vertical-align:-1.329483em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8478869999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdl" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.329483em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqcu" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span></p>
<h3>උපයෝගීතාව(ගෙවන්න)</h3>
<p><a href="#terminal_utility">පර්යන්ත උපයෝගීතාව</a> යනු පර්යන්ත ඉතිහාසයක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> සඳහා ක්රීඩකයෙකුගේ උපයෝගීතාව (හෝ ගෙවීම) <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span>ය. </p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span> කොහේද <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqej" style="margin-right:0.07153em">Z</span></span></span></span></span></span></span></p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqcy" style=""><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="mclose" style="">)</span></span></span></span></span></span> උපාය මාර්ග පැතිකඩ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> සහිත ක්රීඩකයා සඳහා අපේක්ෂිත උපයෝගීතාව (ගෙවීම්) <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span></span></span></span>වේ. </p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqcy" style=""><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.3794880000000003em;vertical-align:-1.329483em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8478869999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdm" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.329483em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqdq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span><span class="mord coloredeq eqcu" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span></p>
<p><a id="NashEquilibrium"></a></p>
<h3>නැෂ්සමතුලිතතාවය</h3>
<p>නැෂ්සමතුලිතතාවය යනු ක්රීඩකයින්ගෙන් කිසිවෙකුට ඔවුන්ගේ උපාය මාර්ගය වෙනස් කිරීමෙන් ඔවුන්ගේ අපේක්ෂිත උපයෝගීතාව (හෝ ගෙවීම්) වැඩි කළ නොහැකි රාජ්යයකි. </p>
<p>ක්රීඩකයන්දෙදෙනෙකු සඳහා, නැෂ් සමතුලිතතාවය යනු <a href="#Strategy">උපාය මාර්ගික පැතිකඩකි</a> </p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0648000000000004em;vertical-align:-1.2824000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7824000000000002em;"><span style="top:-3.9424em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="mclose">)</span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2824000000000002em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7824000000000002em;"><span style="top:-3.9424em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.52566em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7416285714285715em;"><span style="top:-2.188485714285714em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3924000000000001em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.52566em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7416285714285715em;"><span style="top:-2.188485714285714em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3924000000000001em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2824000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqdh" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span>-නැෂ් සමතුලිතතාවය,</p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0648000000000004em;vertical-align:-1.2824000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7824000000000002em;"><span style="top:-3.9424em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqdh" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqdh" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2824000000000002em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7824000000000002em;"><span style="top:-3.9424em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.52566em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7416285714285715em;"><span style="top:-2.188485714285714em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3924000000000001em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.52566em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7416285714285715em;"><span style="top:-2.188485714285714em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3924000000000001em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2824000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><h3>අවමකිරීම කනගාටු</h3>
<p>කනගාටුවවන්නේ උපයෝගීතාව (හෝ ගෙවීම) ක්රීඩකයාට නොලැබුනේ ඇය ප්රශස්ත උපාය මාර්ගයක් අනුගමනය නොකිරීම හෝ හොඳම පියවර ගැනීම නිසාය. </p>
<p>ක්රීඩකයා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> සඳහා සාමාන්ය සමස්ත කනගාටුව පුනරාවර්තන සෑම <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqei" style=""><span class="mord mathnormal" style="margin-right:0.13889em">T</span></span></span></span></span></span> වටයකම ප්රශස්ත උපාය අනුගමනය නොකිරීම පිළිබඳ සාමාන්ය කනගාටුවයි. </p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.138331em;vertical-align:-0.247em;"></span><span class="mord coloredeq eqdt" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcz" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.177714285714286em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mbin mtight" style="">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3222857142857143em;"><span></span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight coloredeq eqdg" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3756em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord coloredeq eqcb" style=""><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqcz" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mbin mtight" style="">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord"><span class="delimsizing size2">)</span></span></span></span></span></span></span></p>
<p>පුනරාවර්තනයේසියලුම ක්රීඩකයින්ගේ උපාය මාර්ග පැතිකඩ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.7935559999999999em;vertical-align:0em;"></span><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span> කොහේද <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord coloredeq eqep" style=""><span class="mord mathnormal" style="">t</span></span></span></span></span></span>, සහ</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.093556em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqcb" style=""><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqcz" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mbin mtight" style="">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span></span></p>
<p>යනු <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>ක්රීඩකයාගේ උපාය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.7935559999999999em;vertical-align:0em;"></span><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span> සමඟ ප්රතිස්ථාපනය කරන ලද උපාය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.94736em;vertical-align:-0.258664em;"></span><span class="mord coloredeq eqcz" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.688696em;"><span style="top:-2.441336em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mbin mtight" style="">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span></span></span></span></span>මාර්ගයයි. </p>
<p>සාමාන්යඋපායමාර්ගය වන්නේ සෑම වටයකදීම අනුගමනය කරන උපාය මාර්ගවල සාමාන්යයයි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.72243em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqcw" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqef" style="margin-right:0.07382em">I</span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span></span></span></span></span></p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.841882em;vertical-align:-1.170941em;"></span><span class="mord coloredeq eqn" style=""><span class="mord" style=""><span class="mord" style="color:cyan"><span class="mord coloredeq eqcf" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqcf" style="">)</span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose coloredeq eqcf" style="">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.670941em;"><span style="top:-2.128769em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mop" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8525400000000001em;"><span style="top:-2.4231360000000004em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7253428571428571em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mop coloredeq eqbd" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9722399999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqbd" style="">(</span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqbd" style="">)</span><span class="mord coloredeq eqbd" style=""><span class="mord" style="color:lightgreen"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:lightgreen">)</span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:lightgreen">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.170941em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></span></p>
<p>ප්රශස්තඋපායමාර්ගය සමඟ සෙල්ලම් නොකිරීමේ මධ්යන්ය කනගාටුව එයයි. </p>
<p>සියලුමක්රීඩකයින් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord coloredeq eqdt" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqdh" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span> සඳහා නම් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqdd" style=""><span class="mord" style="">2</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdh" style="">ϵ</span></span></span></span></span></span></span>-නැෂ් සමතුලිතතාවයකි. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span> </p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:8.342229em;vertical-align:-3.9211145000000007em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.4211145em;"><span style="top:-7.3581195em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord coloredeq eqdt" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-4.8697835em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord coloredeq eqdt" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-1.4743344999999994em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.9211145000000007em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.4211145em;"><span style="top:-7.3581195em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqdh" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span><span style="top:-4.8697835em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcz" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.177714285714286em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mbin mtight" style="">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3222857142857143em;"><span></span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight coloredeq eqdg" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3756em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord coloredeq eqcb" style=""><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqcz" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mbin mtight" style="">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord"><span class="delimsizing size2">)</span></span></span></span><span style="top:-1.4743344999999994em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcz" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.177714285714286em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mbin mtight" style="">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3222857142857143em;"><span></span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight coloredeq eqdg" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3756em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord coloredeq eqcb" style=""><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqcz" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mbin mtight" style="">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqdh" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.9211145000000007em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>එයශුන්ය මුදලක් ක්රීඩාවක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em;"></span><span class="mord">−</span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span> බැවින්, අපට එකතු කළ හැකි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0894389999999998em;vertical-align:-0.24810799999999997em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.4518920000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em;"><span></span></span></span></span></span></span></span></span></span></span> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord coloredeq eqdt" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span></span></span></span></span> අතර දෙවන වාරය අවලංගු වේ. </p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.395449em;vertical-align:-1.4477245em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9477245em;"><span style="top:-3.9477245em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord coloredeq eqdd" style=""><span class="mord" style="">2</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdh" style="">ϵ</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.4477245em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9477245em;"><span style="top:-3.9477245em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdp" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.188485714285714em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.36806em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdp" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.188485714285714em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.36806em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.4477245em;"><span></span></span></span></span></span></span></span></span></span></span></span></span>උපාය මාර්ග<p>සමූහයක් පුරා උපයෝගිතා වල සාමාන්යය සාමාන්ය උපාය මාර්ගයේ උපයෝගීතාවයට සමාන වේ. </p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></span></p>
<p>එබැවින්,</p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.5593910000000002em;vertical-align:-0.5296955em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0296955000000003em;"><span style="top:-3.1383645000000002em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqdd" style=""><span class="mord" style="">2</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdh" style="">ϵ</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5296955em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0296955000000003em;"><span style="top:-3.1383645000000002em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdp" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.188485714285714em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.36806em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdp" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.188485714285714em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.36806em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">2</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5296955em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>අර්ථදැක්වීමෙන් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span></span></span></span></span>, <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.259391em;vertical-align:-0.36806em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdp" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.188485714285714em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.36806em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">2</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-0.25em;"></span><span class="mord">−</span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></span></p>
<p>එවිට,</p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.1187820000000004em;vertical-align:-1.3093910000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8093910000000002em;"><span style="top:-3.91806em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqdd" style=""><span class="mord" style="">2</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdh" style="">ϵ</span></span></span></span></span><span style="top:-2.358669em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqdd" style=""><span class="mord" style="">2</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdh" style="">ϵ</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.3093910000000002em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8093910000000002em;"><span style="top:-3.91806em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdp" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.188485714285714em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.36806em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">−</span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-2.358669em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdp" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6771428571428572em;"><span style="top:-2.188485714285714em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-2.8448em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.31151428571428574em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight"><span class="mord mtight">Σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.36806em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7386959999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.3093910000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>මෙය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqdd" style=""><span class="mord" style="">2</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdh" style="">ϵ</span></span></span></span></span></span></span>-නැෂ් සමතුලිතතාවයයි. ඔබට ඒ හා සමානව ක්රීඩකයින් 2 කට වඩා ඇති ක්රීඩා සඳහා ඔප්පු කළ හැකිය. </p>
<p>එබැවින්නැෂ් සමතුලිතතාවයකට සමීප <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord coloredeq eqdt" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span></span></span></span></span> වීමට අප අවම කළ යුතුය. </p>
<p><a id="CounterfactualRegret"></a></p>
<h3>ප්රතිවිරුද්ධකනගාටුව</h3>
<p><strong>Counterfactualඅගය</strong> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord" style="color:pink"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span></span></span></span></span></span> ක්රීඩකයා ළඟා වීමට <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> උත්සාහ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> නම් ක්රීඩකයා සඳහා අපේක්ෂිත උපයෝගීතාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span></span></span> (ක්රියා ගෙන ක සම්භාවිතාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span></span></span> සමග ප්රමුඛ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqed" style=""><span class="mord" style="">1</span></span></span></span></span></span>). </p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord" style="color:pink"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.444646em;vertical-align:-1.394641em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqeq" style=""><span class="mord mathnormal mtight" style="margin-right:0.04398em">z</span></span><span class="mrel mtight">∈</span><span class="mord mtight coloredeq eqea" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3567071428571427em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.394641em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714392em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcx" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdx" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">]</span></span><span class="mclose">)</span><span class="mord coloredeq eqcj" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqdx" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mopen coloredeq eqdx" style="">[</span><span class="mord coloredeq eqdx" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqdx" style="">]</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqeq" style=""><span class="mord mathnormal" style="margin-right:0.04398em">z</span></span><span class="mclose">)</span></span></span></span></span></span></p>
<p>පර්යන්තඉතිහාස කට්ටලය වෙත ළඟා විය හැකි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span></span></span>අතර <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdx" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">]</span></span></span></span></span></span> එය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqeq" style=""><span class="mord mathnormal" style="margin-right:0.04398em">z</span></span></span></span></span></span> දක්වා උපසර්ගය වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqea" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span></span></span>. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqcj" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqdx" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mopen coloredeq eqdx" style="">[</span><span class="mord coloredeq eqdx" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqdx" style="">]</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span></span></span></span></span> සිට z වෙත ළඟා වීමේ සම්භාවිතාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdx" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">]</span></span></span></span></span></span>වේ. </p>
<p><strong>ක්ෂණිකප්රතිවිරුද්ධ කනගාටුව</strong> නම්,</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.274439em;vertical-align:-0.383108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mord mathnormal mtight">mm</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.274439em;vertical-align:-0.383108em;"></span><span class="mord"><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqek" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="mrel mtight">∈</span><span class="mord mathnormal mtight">A</span><span class="mord mtight"><span class="mord mtight coloredeq eqef" style=""><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.17737em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mord mathnormal mtight">mm</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span></span></span></span></p>
<p>කොහේද</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.274439em;vertical-align:-0.383108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mord mathnormal mtight">mm</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord" style="color:pink"><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mord" style="color:pink"><span class="mord" style="">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mrel mtight" style="">→</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span><span class="mord"><span class="delimsizing size2">)</span></span></span></span></span></span></span></p>
<p>තොරතුරුකට්ටලයේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqef" style=""><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span><span class="mrel mtight">→</span><span class="mord mtight coloredeq eqek" style=""><span class="mord mathnormal mtight" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span> සෑම විටම පියවර <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span></span></span></span></span> ගැනීම වෙනස් කිරීම <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqdp" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span></span></span></span></span></span> සමඟ උපාය පැතිකඩ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span></span></span>කොහේද? </p>
<p><a href="http://martin.zinkevich.org/publications/regretpoker.pdf">පත්රිකාව</a> එය සනාථ කරයි (ප්රමේයය 3),</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.138331em;vertical-align:-0.247em;"></span><span class="mord coloredeq eqdt" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.3717110000000003em;vertical-align:-1.321706em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8556639999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqef" style=""><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span><span class="mrel mtight">∈</span><span class="mord mtight coloredeq eqcw" style=""><span class="mord mtight" style=""><span class="mord mathcal mtight coloredeq eqef" style="margin-right:0.07382em">I</span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.321706em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mord mathnormal mtight">mm</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight">,</span><span class="mord mtight">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.412972em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span></span></span></span></span></span> කොහේද <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.372211em;vertical-align:-0.412972em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mord mathnormal mtight">mm</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight">,</span><span class="mord mtight">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.412972em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.274439em;vertical-align:-0.383108em;"></span><span class="mord coloredeq eqdv" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mpunct mtight">,</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mord mathnormal mtight">mm</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></span></p>
<p><a id="RegretMatching"></a></p>
<h3>කනගාටුගැලපීම</h3>
<p>උපායමාර්ගයගණනය කරනු ලබන්නේ කනගාටු ගැලපීම භාවිතා කරමිනි. </p>
<p>එක්එක් තොරතුරු කට්ටලය සහ ක්රියාකාරී යුගලය සඳහා කනගාටුව පවත්වා ගෙන <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span> යනු ලැබේ,</p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:4.899005000000001em;vertical-align:-2.1995025000000004em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.6995025000000004em;"><span style="top:-5.6842825em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord" style="color:coral"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8435559999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-3.1959465em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.1995025000000004em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.6995025000000004em;"><span style="top:-5.6842825em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mord" style="color:pink"><span class="mord" style="">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mrel mtight" style="">→</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span></span></span><span style="top:-3.1959465em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:coral"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8435559999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.1995025000000004em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>උපායමාර්ගයගණනය කරනු ලබන්නේ කනගාටු ගැලපීමෙන්,</p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.9000399999999997em;vertical-align:-1.70002em;"></span><span class="mord coloredeq eqb" style=""><span class="mord" style=""><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.2000199999999994em;"><span style="top:-4.200019999999999em;"><span class="pstrut" style="height:4.05002em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mbin mtight" style="">+</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:lightgreen">)</span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:lightgreen">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="minner" style=""><span class="mopen" style=""><span class="delimsizing mult" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em;"><span style="top:-2.49999em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.49199em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.016em;width:0.889em"><svg height="0.016em" preserveaspectratio="xMinYMin" style="width:0.889em" viewbox="0 0 889 16" width="0.889em" xmlns="http://www.w3.org/2000/svg"><path d="M384 0 H504 V16 H384z M384 0 H504 V16 H384z"></path></svg></span></span><span style="top:-3.15001em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.292009999999999em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.016em;width:0.889em"><svg height="0.016em" preserveaspectratio="xMinYMin" style="width:0.889em" viewbox="0 0 889 16" width="0.889em" xmlns="http://www.w3.org/2000/svg"><path d="M384 0 H504 V16 H384z M384 0 H504 V16 H384z"></path></svg></span></span><span style="top:-4.30002em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0420485em;"><span style="top:-4.0420485em;"><span class="pstrut" style="height:3.215845em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2158449999999998em;"><span style="top:-2.509755em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mop mtight coloredeq eqbi" style=""><span class="mop op-symbol small-op mtight" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.28539000000000003em;"><span style="top:-2.2853899999999996em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.6068285714285713em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8495600000000001em;"><span style="top:-2.84956em;margin-right:0.1em;"><span class="pstrut" style="height:2.55556em;"></span><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span><span class="mrel mtight" style="">∈</span><span class="mord mathnormal mtight" style="">A</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000100000000001em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.19516666666666668em"></span><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9717785714285714em;"><span style="top:-2.177714285714286em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-2.9836857142857145em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.32228571428571423em;"><span></span></span></span></span></span></span><span class="mopen mtight" style="color:orange">(</span><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct mtight" style="color:orange">,</span><span class="mord mtight" style="color:orange"><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mclose mtight" style="color:orange">)</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5356em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9717785714285714em;"><span style="top:-2.177714285714286em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-2.9836857142857145em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3222857142857143em;"><span></span></span></span></span></span></span><span class="mopen mtight" style="color:orange">(</span><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct mtight" style="color:orange">,</span><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="mclose mtight" style="color:orange">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8402519999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct" style="">,</span></span></span><span style="top:-2.1937965em;"><span class="pstrut" style="height:3.215845em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mopen mtight coloredeq eqcl" style="">∣</span><span class="mord mathnormal mtight coloredeq eqcl" style="">A</span><span class="mopen mtight coloredeq eqcl" style="">(</span><span class="mord mtight coloredeq eqcl" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight coloredeq eqcl" style="">)∣</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct" style="">,</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5420485em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0420485em;"><span style="top:-4.0420485em;"><span class="pstrut" style="height:3.215845em;"></span><span class="mord" style=""><span class="mord text" style=""><span class="mord" style=""><span class="mord coloredeq eqen" style="">i</span></span><span class="mord" style="">f</span></span><span class="mord" style=""><span class="mord coloredeq eqbg" style=""><span class="mop coloredeq eqbi" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.22528999999999993em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mrel mtight" style="">∈</span><span class="mord mathnormal mtight" style="">A</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.47471em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mclose" style="color:orange">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel coloredeq eqbg" style="">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord coloredeq eqbg" style="">0</span></span></span></span><span style="top:-2.1937965em;"><span class="pstrut" style="height:3.215845em;"></span><span class="mord" style=""><span class="mord text" style=""><span class="mord" style="">o</span><span class="mord" style=""><span class="mord coloredeq eqep" style="">t</span></span><span class="mord" style=""><span class="mord coloredeq eqem" style="">h</span></span><span class="mord" style="">erw</span><span class="mord" style=""><span class="mord coloredeq eqen" style="">i</span></span><span class="mord" style="">se</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5420485em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.70002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span><p>කොහේද <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord"><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:orange">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel coloredeq eqz" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqz" style=""><span class="mop coloredeq eqdv" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="mord coloredeq eqz" style=""><span class="delimsizing size2" style=""><span style="">(</span></span></span><span class="mord coloredeq eqz" style=""><span class="mord" style="color:orange"><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:orange">)</span></span><span class="mpunct coloredeq eqz" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqz" style="">0</span><span class="mord coloredeq eqz" style=""><span class="delimsizing size2" style=""><span style="">)</span></span></span></span></span></span></span></span></p>
<p>කඩදාසි <a href="http://martin.zinkevich.org/publications/regretpoker.pdf">අසම්පූර්ණ තොරතුරු සහිත ක්රීඩා වල කනගාටුව අවම කිරීම ඉහත සමීකරණයට</a> අනුව උපාය මාර්ගය තෝරා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord coloredeq eqdt" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span></span></span></span></span> ගන්නේ නම් ඊට සමානුපාතිකව කුඩා වන බව ඔප්පු කරයි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.383108em;vertical-align:-0.538em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.537397em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9322900000000001em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight coloredeq eqei" style="padding-left:0.833em"><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span><span style="top:-2.89229em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.10770999999999997em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, එබැවින් ළඟා වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqdh" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span>-<a href="#NashEquilibrium">නෂ් සමතුලිතතාවය</a>. </p>
<p><a id="MCCFR"></a></p>
<h3>මොන්ටේකාලෝ CFR (MCCFR)</h3>
<p>පරිගණකකරණයටඑක් එක් පුනරාවර්තනයේ සම්පූර්ණ ක්රීඩා ගස පුළුල් කිරීම <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.05222em;vertical-align:-0.258664em;"></span><span class="mord" style="color:coral"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-2.441336em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span> අවශ්ය වේ. </p>
<p><a href="http://mlanctot.info/files/papers/nips09mccfr.pdf">පුළුල් ක්රීඩා වල කනගාටුව අවම කිරීම සඳහා කඩදාසි මොන්ටේ කාලෝ නියැදීම අපට ක්රීඩා</a> ගසෙන් සාම්පල ලබා ගත හැකි අතර කනගාටුව තක්සේරු කළ හැකිය. </p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.78055em;vertical-align:-0.09722em;"></span><span class="mord mathcal">Q</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> යනු උප කට්ටල සමූහයකි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqej" style=""><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span></span></span></span></span> (<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord coloredeq eqdz" style=""><span class="mord" style=""><span class="mord mathnormal" style="">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">⊆</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqej" style=""><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span></span></span></span></span>) එහිදී අපි පුනරාවර්තනයක තනි බ්ලොක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord coloredeq eqdz" style=""><span class="mord" style=""><span class="mord mathnormal" style="">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></span></span> එකක් පමණක් දෙස බලමු. සියලුම උප කුලවල සංගමය විහිදේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqej" style=""><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span></span></span></span></span> (<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∩</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.55556em;vertical-align:0em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∩</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqej" style=""><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span></span></span></span></span>). <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord coloredeq eqec" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></span></span> බ්ලොක් තෝරා ගැනීමේ සම්භාවිතාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord coloredeq eqdz" style=""><span class="mord" style=""><span class="mord mathnormal" style="">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></span></span>. </p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span></span></span></span></span> වත්මන් පුනරාවර්තනයේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqeq" style=""><span class="mord mathnormal" style="margin-right:0.04398em">z</span></span></span></span></span></span> දී තෝරා ගැනීමේ සම්භාවිතාව; i.e. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.24703em;vertical-align:-0.49703em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.17862099999999997em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqeo" style=""><span class="mord mathnormal mtight" style="margin-right:0.05724em">j</span></span><span class="mrel mtight">:</span><span class="mord mtight coloredeq eqde" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdz" style=""><span class="mord mathnormal mtight" style="">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2818857142857143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.49703em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqec" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></span></span> - <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord coloredeq eqec" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></span></span> කොතැනද එකතුව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em;"></span><span class="mord coloredeq eqde" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord coloredeq eqdz" style=""><span class="mord mathnormal" style="">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></span></span></span>. </p>
<p>එවිටඅපි වාරණ සිට <strong>sampled counterfactual අගය</strong> ලබා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqeo" style=""><span class="mord mathnormal" style="margin-right:0.05724em">j</span></span></span></span></span></span>,</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord accent" style="color:pink"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord mathnormal" style="margin-right:0.03588em;color:pink">σ</span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mord" style="color:pink">∣</span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqeo" style="margin-right:0.05724em">j</span></span><span class="mclose" style="color:pink">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.813096em;vertical-align:-1.491656em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8556639999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqde" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdz" style=""><span class="mord mathnormal mtight" style="">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2818857142857143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.491656em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqdw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqed" style=""><span class="mord" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714392em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcx" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqdx" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">]</span></span><span class="mclose">)</span><span class="mord coloredeq eqcj" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqdx" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mopen coloredeq eqdx" style="">[</span><span class="mord coloredeq eqdx" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqdx" style="">]</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span><span class="mord"><span class="mord mathnormal">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqeq" style=""><span class="mord mathnormal" style="margin-right:0.04398em">z</span></span><span class="mclose">)</span></span></span></span></span></span></p>
<p>කඩදාසිබව පෙන්නුම්</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord"><span class="mord mathbb">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166400000000005em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqeo" style=""><span class="mord mathnormal mtight" style="margin-right:0.05724em">j</span></span><span class="mrel mtight">∼</span><span class="mord mtight coloredeq eqec" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeo" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2818857142857143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.34731999999999996em;"><span></span></span></span></span></span></span><span class="mord"><span class="delimsizing size2">[</span></span><span class="mord accent" style="color:pink"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord mathnormal" style="margin-right:0.03588em;color:pink">σ</span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mord" style="color:pink">∣</span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqeo" style="margin-right:0.05724em">j</span></span><span class="mclose" style="color:pink">)</span><span class="mord"><span class="delimsizing size2">]</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord" style="color:pink"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span></p>
<p>සරලසාක්ෂියක් සමඟ. </p>
<p>එබැවින්අපට ක්රීඩා ගසේ කොටසක් සාම්පල ගත කර කනගාටු ගණනය කළ හැකිය. කනගාටුව පිළිබඳ ඇස්තමේන්තුවක් අපි ගණනය කරමු</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.093556em;vertical-align:-0.25em;"></span><span class="mord" style="color:coral"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8435559999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="color:coral">(</span><span class="mord" style="color:coral"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:coral">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:coral"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:coral">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.093556em;vertical-align:-0.25em;"></span><span class="mord" style="color:pink"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mord" style="color:pink"><span class="mord" style="">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mrel mtight" style="">→</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.093556em;vertical-align:-0.25em;"></span><span class="mord" style="color:pink"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span></span></span></span></span></span></p>
<p>එක්එක් පුනරාවර්තනයේ උපාය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0913309999999998em;vertical-align:-0.25em;"></span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mbin mtight" style="">+</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span> යාවත්කාලීන කිරීමට <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span> සහ ගණනය කිරීමට එය භාවිතා කරන්න. අවසාන වශයෙන්, අපි සමස්ත සාමාන්ය උපාය ගණනය කරමු <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord" style="color:cyan"><span class="mord" style=""><span class="mord coloredeq eqcf" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqcf" style="">)</span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose coloredeq eqcf" style="">)</span></span></span></span></span></span></span>. </p>
<p>මෙන්න <a href="kuhn/index.html">කුහ්න් පෝකර්</a> මත CFR උත්සාහ කිරීමට Kuhn පෝකර් ක්රියාත්මක කිරීම. </p>
අපි<p><em>කේතයට කිමිදෙමු! </em></p>

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            <div class="highlight"><pre><span class="lineno">328</span><span></span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">NewType</span><span class="p">,</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">List</span><span class="p">,</span> <span class="n">Callable</span><span class="p">,</span> <span class="n">cast</span>
<span class="lineno">329</span>
<span class="lineno">330</span><span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">monit</span><span class="p">,</span> <span class="n">tracker</span><span class="p">,</span> <span class="n">logger</span><span class="p">,</span> <span class="n">experiment</span>
<span class="lineno">331</span><span class="kn">from</span> <span class="nn">labml.configs</span> <span class="kn">import</span> <span class="n">BaseConfigs</span><span class="p">,</span> <span class="n">option</span></pre></div>
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    <div class='section' id='section-1'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-1'>#</a>
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            <p>ක්රීඩකයන්ගේකට්ටලය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.72243em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdn" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqen" style="">i</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeg" style="margin-right:0.10903em">N</span></span></span></span></span></span></span> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqeg" style=""><span class="mord mathnormal" style="margin-right:0.10903em">N</span></span></span></span></span></span> කොහෙද ක්රීඩකයෙක් </p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">334</span><span class="n">Player</span> <span class="o">=</span> <span class="n">NewType</span><span class="p">(</span><span class="s1">&#39;Player&#39;</span><span class="p">,</span> <span class="nb">int</span><span class="p">)</span></pre></div>
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    <div class='section' id='section-2'>
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            <div class='section-link'>
                <a href='#section-2'>#</a>
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            <p>ක්රියාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span></span></span></span></span>, පර්යන්ත <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdk" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqee" style="margin-right:0.08125em">H</span></span></span></span></span></span></span> නොවන <a href="#History">ඉතිහාසයක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqce" style=""><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel" style="">:</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqee" style="margin-right:0.08125em">H</span></span></span></span></span></span></span></span> </a> කොහේද? </p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">336</span><span class="n">Action</span> <span class="o">=</span> <span class="n">NewType</span><span class="p">(</span><span class="s1">&#39;Action&#39;</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-3'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-3'>#</a>
            </div>
            <p> <a id="History"></a></p>
<h2>ඉතිහාසය</h2>
<p>ඉතිහාසය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdk" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqee" style="margin-right:0.08125em">H</span></span></span></span></span></span></span> යනු ඇතුළු ක්රියා වල අනුක්රමයකි අවස්ථාවක් සිදුවීම්, <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqee" style=""><span class="mord mathnormal" style="margin-right:0.08125em">H</span></span></span></span></span></span> එය සියලු ඉතිහාසයන්ගේ සමූහයයි. </p>
<p>මෙමපන්තිය ක්රීඩා විශේෂිත තර්කනය සමඟ දීර් can කළ යුතුය. </p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">339</span><span class="k">class</span> <span class="nc">History</span><span class="p">:</span></pre></div>
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        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-4'>#</a>
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            <p> එයපර්යන්ත ඉතිහාසයක් වේවා; එනම් ක්රීඩාව අවසන්. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqej" style="margin-right:0.07153em">Z</span></span></span></span></span></span></span></p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">351</span>    <span class="k">def</span> <span class="nf">is_terminal</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
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    <div class='section' id='section-5'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-5'>#</a>
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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">356</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
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                <a href='#section-6'>#</a>
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            <p> <a id="terminal_utility"></a> පර්යන්ත ඉතිහාසයක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> සඳහා ක්රීඩකයාගේ උපයෝගීතාව. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span> කොහේද <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqej" style="margin-right:0.07153em">Z</span></span></span></span></span></span></span></p>

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            <div class="highlight"><pre><span class="lineno">358</span>    <span class="k">def</span> <span class="nf">terminal_utility</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">Player</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span></pre></div>
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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">364</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
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            <p> වත්මන්ක්රීඩකයා ලබා ගන්න, විසින් දැක්වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdu" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqeh" style="margin-right:0.13889em">P</span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span>, එහිදී <strong>ක්රීඩකයා උත්සවය</strong>ලෙස <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqeh" style=""><span class="mord mathnormal" style="margin-right:0.13889em">P</span></span></span></span></span></span> හැඳින්වේ. </p>
<p>වර්තමාන <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqel" style=""><span class="mord mathnormal" style="">c</span></span></span></span></span></span> සිදුවීම අවස්ථාවක් අවස්ථාවක් බව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdf" style=""><span class="mord" style=""><span class="mord coloredeq eqdu" style=""><span class="mord mathnormal coloredeq eqeh" style="margin-right:0.13889em">P</span></span><span class="mopen coloredeq eqdu" style="">(</span><span class="mord coloredeq eqdu" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose coloredeq eqdu" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqel" style="">c</span></span></span></span></span></span></span> එයින් අදහස් කරන්නේ නම්. කාඩ්පත් ගනුදෙනු කිරීම හෝ පෝකර් වල පොදු කාඩ්පත් විවෘත කිරීම වැනි දෙයක්. </p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">366</span>    <span class="k">def</span> <span class="nf">player</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Player</span><span class="p">:</span></pre></div>
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            <div class='section-link'>
                <a href='#section-9'>#</a>
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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">373</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
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    <div class='section' id='section-10'>
        <div class='docs doc-strings'>
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                <a href='#section-10'>#</a>
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            <p> ඊළඟපියවර අහම්බෙන් පියවරක් වේවා; නව කාඩ්පතක් ගනුදෙනු කිරීම වැනි දෙයක්. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdf" style=""><span class="mord" style=""><span class="mord coloredeq eqdu" style=""><span class="mord mathnormal coloredeq eqeh" style="margin-right:0.13889em">P</span></span><span class="mopen coloredeq eqdu" style="">(</span><span class="mord coloredeq eqdu" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose coloredeq eqdu" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqel" style="">c</span></span></span></span></span></span></span></p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">375</span>    <span class="k">def</span> <span class="nf">is_chance</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span></pre></div>
        </div>
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    <div class='section' id='section-11'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-11'>#</a>
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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">380</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
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    <div class='section' id='section-12'>
        <div class='docs doc-strings'>
            <div class='section-link'>
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            <p> කවදාදඅවස්ථාවක් සාම්පලය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdf" style=""><span class="mord" style=""><span class="mord coloredeq eqdu" style=""><span class="mord mathnormal coloredeq eqeh" style="margin-right:0.13889em">P</span></span><span class="mopen coloredeq eqdu" style="">(</span><span class="mord coloredeq eqdu" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose coloredeq eqdu" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqel" style="">c</span></span></span></span></span></span></span>. </p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">382</span>    <span class="k">def</span> <span class="nf">sample_chance</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Action</span><span class="p">:</span></pre></div>
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    <div class='section' id='section-13'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-13'>#</a>
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        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">386</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
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        <div class='docs doc-strings'>
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            <p> ඉතිහාසයටක්රියාවක් එක් කරන්න. </p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">388</span>    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">action</span><span class="p">:</span> <span class="n">Action</span><span class="p">):</span></pre></div>
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    <div class='section' id='section-15'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-15'>#</a>
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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">392</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
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    <div class='section' id='section-16'>
        <div class='docs doc-strings'>
            <div class='section-link'>
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            <p> වත්මන්ක්රීඩකයා <a href="#InfoSet">සඳහා තොරතුරු</a> ලබා ගන්න</p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">394</span>    <span class="k">def</span> <span class="nf">info_set_key</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span></pre></div>
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                <a href='#section-17'>#</a>
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        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">398</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span></pre></div>
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    <div class='section' id='section-18'>
        <div class='docs doc-strings'>
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                <a href='#section-18'>#</a>
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            <p> වත්මන්ක්රීඩකයා සඳහා නව <a href="#InfoSet">තොරතුරු කට්ටලයක්</a> සාදන්න</p>

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            <div class="highlight"><pre><span class="lineno">400</span>    <span class="k">def</span> <span class="nf">new_info_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s1">&#39;InfoSet&#39;</span><span class="p">:</span></pre></div>
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    <div class='section' id='section-19'>
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                <a href='#section-19'>#</a>
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            <div class="highlight"><pre><span class="lineno">404</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
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            <div class='section-link'>
                <a href='#section-20'>#</a>
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            <p> මානවකියවිය හැකි නිරූපණය</p>

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            <div class="highlight"><pre><span class="lineno">406</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
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            <div class='section-link'>
                <a href='#section-21'>#</a>
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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">410</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
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                <a href='#section-22'>#</a>
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            <p> <a id="InfoSet"></a></p>
<h2>තොරතුරුකට්ටලය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdy" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></h2>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">413</span><span class="k">class</span> <span class="nc">InfoSet</span><span class="p">:</span></pre></div>
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    <div class='section' id='section-23'>
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            <div class='section-link'>
                <a href='#section-23'>#</a>
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            <p>අද්විතීයයතුර තොරතුරු කට්ටලය හඳුනා ගැනීම </p>

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            <div class="highlight"><pre><span class="lineno">421</span>    <span class="n">key</span><span class="p">:</span> <span class="nb">str</span></pre></div>
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            <div class='section-link'>
                <a href='#section-24'>#</a>
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            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>, ක්රීඩකයාගේ <a href="#Strategy">උපාය</a> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> </p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">423</span>    <span class="n">strategy</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Action</span><span class="p">,</span> <span class="nb">float</span><span class="p">]</span></pre></div>
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    <div class='section' id='section-25'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-25'>#</a>
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            <p>එක්එක් පියවර නොගැනීම පිළිබඳ සම්පූර්ණ කනගාටුව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdo" style=""><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqdy" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span>,</p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:4.899005000000001em;vertical-align:-2.1995025000000004em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.6995025000000004em;"><span style="top:-5.6842825em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord" style="color:coral"><span class="mord" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8435559999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span><span style="top:-3.1959465em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.1995025000000004em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.6995025000000004em;"><span style="top:-5.6842825em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="color:pink"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mord" style="color:pink"><span class="mord" style="">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mrel mtight" style="">→</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style="color:pink"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span></span></span><span style="top:-3.1959465em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqed" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:coral"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8435559999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="color:coral">(</span><span class="mord" style="color:coral"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:coral">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:coral"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:coral">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.1995025000000004em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>පරිගණකඋපාය විට <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.190108em;vertical-align:-0.345em;"></span><span class="mord coloredeq eqcv" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span> කාලීන කෙසේ හෝ සිදු අවලංගු <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span> සිට අපි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord coloredeq eqbt" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mord" style=""><span class="mord" style="color:orange"><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:orange">)</span></span></span></span></span></span></span> ඒ වෙනුවට පවත්වාගෙන <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0913309999999998em;vertical-align:-0.25em;"></span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mbin mtight" style="">+</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span> 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            <div class="highlight"><pre><span class="lineno">438</span>    <span class="n">regret</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Action</span><span class="p">,</span> <span class="nb">float</span><span class="p">]</span></pre></div>
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    <div class='section' id='section-26'>
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            <div class='section-link'>
                <a href='#section-26'>#</a>
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            <p>සමස්තසාමාන්ය උපායමාර්ගය ගණනය <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mord coloredeq eqbd" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord" style="color:lightgreen"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:lightgreen">)</span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:lightgreen">)</span></span></span></span></span></span></span></span> කිරීම සඳහා අපි සමුච්චිත උපාය මාර්ගය පවත්වා ගනිමු</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.841882em;vertical-align:-1.170941em;"></span><span class="mord coloredeq eqn" style=""><span class="mord" style=""><span class="mord" style="color:cyan"><span class="mord coloredeq eqcf" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqcf" style="">)</span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose coloredeq eqcf" style="">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.670941em;"><span style="top:-2.128769em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mop" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8525400000000001em;"><span style="top:-2.4231360000000004em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7253428571428571em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mop coloredeq eqbd" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9722399999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqbd" style="">(</span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqbd" style="">)</span><span class="mord coloredeq eqbd" style=""><span class="mord" style="color:lightgreen"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:lightgreen">)</span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:lightgreen">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.170941em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">445</span>    <span class="n">cumulative_strategy</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Action</span><span class="p">,</span> <span class="nb">float</span><span class="p">]</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-27'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-27'>#</a>
            </div>
            <p> ආරම්භකරන්න</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">447</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-28'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-28'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">451</span>        <span class="bp">self</span><span class="o">.</span><span class="n">key</span> <span class="o">=</span> <span class="n">key</span>
<span class="lineno">452</span>        <span class="bp">self</span><span class="o">.</span><span class="n">regret</span> <span class="o">=</span> <span class="p">{</span><span class="n">a</span><span class="p">:</span> <span class="mi">0</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">actions</span><span class="p">()}</span>
<span class="lineno">453</span>        <span class="bp">self</span><span class="o">.</span><span class="n">cumulative_strategy</span> <span class="o">=</span> <span class="p">{</span><span class="n">a</span><span class="p">:</span> <span class="mi">0</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">actions</span><span class="p">()}</span>
<span class="lineno">454</span>        <span class="bp">self</span><span class="o">.</span><span class="n">calculate_strategy</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-29'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-29'>#</a>
            </div>
            <p> ක්‍රියා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdo" style=""><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqdy" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">456</span>    <span class="k">def</span> <span class="nf">actions</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Action</span><span class="p">]:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-30'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-30'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">460</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-31'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-31'>#</a>
            </div>
            <p> සුරකිනලද ශබ්දකෝෂයකින් තොරතුරු කට්ටලය පූරණය කරන්න</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">462</span>    <span class="nd">@staticmethod</span>
<span class="lineno">463</span>    <span class="k">def</span> <span class="nf">from_dict</span><span class="p">(</span><span class="n">data</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="s1">&#39;InfoSet&#39;</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-32'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-32'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">467</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-33'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-33'>#</a>
            </div>
            <p> ශබ්දකෝෂයකට සකසා ඇති තොරතුරු සුරකින්න</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">469</span>    <span class="k">def</span> <span class="nf">to_dict</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-34'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-34'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">473</span>        <span class="k">return</span> <span class="p">{</span>
<span class="lineno">474</span>            <span class="s1">&#39;key&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">key</span><span class="p">,</span>
<span class="lineno">475</span>            <span class="s1">&#39;regret&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">regret</span><span class="p">,</span>
<span class="lineno">476</span>            <span class="s1">&#39;average_strategy&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">cumulative_strategy</span><span class="p">,</span>
<span class="lineno">477</span>        <span class="p">}</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-35'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-35'>#</a>
            </div>
            <p> සුරකිනලද ශබ්දකෝෂයකින් දත්ත පූරණය කරන්න</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">479</span>    <span class="k">def</span> <span class="nf">load_dict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">]):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-36'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-36'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">483</span>        <span class="bp">self</span><span class="o">.</span><span class="n">regret</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="s1">&#39;regret&#39;</span><span class="p">]</span>
<span class="lineno">484</span>        <span class="bp">self</span><span class="o">.</span><span class="n">cumulative_strategy</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="s1">&#39;average_strategy&#39;</span><span class="p">]</span>
<span class="lineno">485</span>        <span class="bp">self</span><span class="o">.</span><span class="n">calculate_strategy</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-37'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-37'>#</a>
            </div>
            <h2>උපායගණනය</h2>
<p><a href="#RegretMatching">කනගාටු ගැලපීම</a>භාවිතා කරමින් වත්මන් උපාය ගණනය කරන්න. </p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.9000399999999997em;vertical-align:-1.70002em;"></span><span class="mord coloredeq eqb" style=""><span class="mord" style=""><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.2000199999999994em;"><span style="top:-4.200019999999999em;"><span class="pstrut" style="height:4.05002em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mbin mtight" style="">+</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:lightgreen">)</span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:lightgreen">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="minner" style=""><span class="mopen" style=""><span class="delimsizing mult" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em;"><span style="top:-2.49999em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.49199em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.016em;width:0.889em"><svg height="0.016em" preserveaspectratio="xMinYMin" style="width:0.889em" viewbox="0 0 889 16" width="0.889em" xmlns="http://www.w3.org/2000/svg"><path d="M384 0 H504 V16 H384z M384 0 H504 V16 H384z"></path></svg></span></span><span style="top:-3.15001em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.292009999999999em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.016em;width:0.889em"><svg height="0.016em" preserveaspectratio="xMinYMin" style="width:0.889em" viewbox="0 0 889 16" width="0.889em" xmlns="http://www.w3.org/2000/svg"><path d="M384 0 H504 V16 H384z M384 0 H504 V16 H384z"></path></svg></span></span><span style="top:-4.30002em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0420485em;"><span style="top:-4.0420485em;"><span class="pstrut" style="height:3.215845em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2158449999999998em;"><span style="top:-2.509755em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mop mtight coloredeq eqbi" style=""><span class="mop op-symbol small-op mtight" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.28539000000000003em;"><span style="top:-2.2853899999999996em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.6068285714285713em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8495600000000001em;"><span style="top:-2.84956em;margin-right:0.1em;"><span class="pstrut" style="height:2.55556em;"></span><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span><span class="mrel mtight" style="">∈</span><span class="mord mathnormal mtight" style="">A</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000100000000001em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.19516666666666668em"></span><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9717785714285714em;"><span style="top:-2.177714285714286em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-2.9836857142857145em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.32228571428571423em;"><span></span></span></span></span></span></span><span class="mopen mtight" style="color:orange">(</span><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct mtight" style="color:orange">,</span><span class="mord mtight" style="color:orange"><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mclose mtight" style="color:orange">)</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5356em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9717785714285714em;"><span style="top:-2.177714285714286em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-2.9836857142857145em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3222857142857143em;"><span></span></span></span></span></span></span><span class="mopen mtight" style="color:orange">(</span><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct mtight" style="color:orange">,</span><span class="mord mtight" style="color:orange"><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="mclose mtight" style="color:orange">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8402519999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct" style="">,</span></span></span><span style="top:-2.1937965em;"><span class="pstrut" style="height:3.215845em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mopen mtight coloredeq eqcl" style="">∣</span><span class="mord mathnormal mtight coloredeq eqcl" style="">A</span><span class="mopen mtight coloredeq eqcl" style="">(</span><span class="mord mtight coloredeq eqcl" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight coloredeq eqcl" style="">)∣</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct" style="">,</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5420485em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0420485em;"><span style="top:-4.0420485em;"><span class="pstrut" style="height:3.215845em;"></span><span class="mord" style=""><span class="mord text" style=""><span class="mord" style=""><span class="mord coloredeq eqen" style="">i</span></span><span class="mord" style="">f</span></span><span class="mord" style=""><span class="mord coloredeq eqbg" style=""><span class="mop coloredeq eqbi" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.22528999999999993em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mrel mtight" style="">∈</span><span class="mord mathnormal mtight" style="">A</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.47471em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mclose" style="color:orange">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel coloredeq eqbg" style="">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord coloredeq eqbg" style="">0</span></span></span></span><span style="top:-2.1937965em;"><span class="pstrut" style="height:3.215845em;"></span><span class="mord" style=""><span class="mord text" style=""><span class="mord" style="">o</span><span class="mord" style=""><span class="mord coloredeq eqep" style="">t</span></span><span class="mord" style=""><span class="mord coloredeq eqem" style="">h</span></span><span class="mord" style="">erw</span><span class="mord" style=""><span class="mord coloredeq eqen" style="">i</span></span><span class="mord" style="">se</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5420485em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.70002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span><p>කොහේද <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord"><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:orange">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel coloredeq eqz" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqz" style=""><span class="mop coloredeq eqdv" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="mord coloredeq eqz" style=""><span class="delimsizing size2" style=""><span style="">(</span></span></span><span class="mord coloredeq eqz" style=""><span class="mord" style="color:orange"><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:orange">)</span></span><span class="mpunct coloredeq eqz" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqz" style="">0</span><span class="mord coloredeq eqz" style=""><span class="delimsizing size2" style=""><span style="">)</span></span></span></span></span></span></span></span></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">487</span>    <span class="k">def</span> <span class="nf">calculate_strategy</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-38'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-38'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord"><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9592389999999998em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.180908em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:orange">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel coloredeq eqz" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqz" style=""><span class="mop coloredeq eqdv" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span></span><span class="mord coloredeq eqz" style=""><span class="delimsizing size2" style=""><span style="">(</span></span></span><span class="mord coloredeq eqz" style=""><span class="mord" style="color:orange"><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:orange">)</span></span><span class="mpunct coloredeq eqz" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqz" style="">0</span><span class="mord coloredeq eqz" style=""><span class="delimsizing size2" style=""><span style="">)</span></span></span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">506</span>        <span class="n">regret</span> <span class="o">=</span> <span class="p">{</span><span class="n">a</span><span class="p">:</span> <span class="nb">max</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">regret</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-39'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-39'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.5660100000000003em;vertical-align:-1.516005em;"></span><span class="mord"><span class="mop op-limits coloredeq eqbi" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.808995em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mrel mtight" style="">∈</span><span class="mord mathnormal mtight" style="">A</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight" style="">)</span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.516005em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9592389999999998em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.180908em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mclose" style="color:orange">)</span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">508</span>        <span class="n">regret_sum</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">regret</span><span class="o">.</span><span class="n">values</span><span class="p">())</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-40'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-40'>#</a>
            </div>
            <p>නම් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.433949em;vertical-align:-0.47471em;"></span><span class="mord coloredeq eqbg" style=""><span class="mord" style=""><span class="mop coloredeq eqbi" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.22528999999999993em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mrel mtight" style="">∈</span><span class="mord mathnormal mtight" style="">A</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.47471em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mclose" style="color:orange">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="">0</span></span></span></span></span></span>, </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">510</span>        <span class="k">if</span> <span class="n">regret_sum</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-41'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-41'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.141331em;vertical-align:-0.25em;"></span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mbin mtight" style="">+</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.960188em;vertical-align:-1.323949em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.636239em;"><span style="top:-2.150761em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mop coloredeq eqbi" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.22528999999999993em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mrel mtight" style="">∈</span><span class="mord mathnormal mtight" style="">A</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose mtight" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.47471em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6778919999999999em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">′</span></span></span></span></span></span></span></span></span><span class="mclose" style="color:orange">)</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.6769999999999996em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.959239em;"><span style="top:-2.4231360000000004em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style="">+</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.323949em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">513</span>            <span class="bp">self</span><span class="o">.</span><span class="n">strategy</span> <span class="o">=</span> <span class="p">{</span><span class="n">a</span><span class="p">:</span> <span class="n">r</span> <span class="o">/</span> <span class="n">regret_sum</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">regret</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-42'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-42'>#</a>
            </div>
            <p>එසේනොමැති නම් </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">515</span>        <span class="k">else</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-43'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-43'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqcl" style=""><span class="mopen" style="">∣</span><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)∣</span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">517</span>            <span class="n">count</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">a</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">regret</span><span class="p">))</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-44'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-44'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.141331em;vertical-align:-0.25em;"></span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdj" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.891331em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mbin mtight" style="">+</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.25744em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqcl" style=""><span class="mopen" style="">∣</span><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)∣</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqed" style=""><span class="mord" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">520</span>            <span class="bp">self</span><span class="o">.</span><span class="n">strategy</span> <span class="o">=</span> <span class="p">{</span><span class="n">a</span><span class="p">:</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">count</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">regret</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-45'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-45'>#</a>
            </div>
            <h2>සාමාන්යඋපාය ලබා ගන්න</h2>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.841882em;vertical-align:-1.170941em;"></span><span class="mord coloredeq eql" style=""><span class="mord" style=""><span class="mord" style="color:cyan"><span class="mord coloredeq eqcf" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqcf" style="">)</span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose coloredeq eqcf" style="">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.670941em;"><span style="top:-2.128769em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mop" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8525400000000001em;"><span style="top:-2.4231360000000004em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7253428571428571em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mop coloredeq eqbd" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9722399999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqbd" style="">(</span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqbd" style="">)</span><span class="mord coloredeq eqbd" style=""><span class="mord" style="color:lightgreen"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:lightgreen">)</span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:lightgreen">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.170941em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></span></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">522</span>    <span class="k">def</span> <span class="nf">get_average_strategy</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-46'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-46'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">531</span>        <span class="n">cum_strategy</span> <span class="o">=</span> <span class="p">{</span><span class="n">a</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">cumulative_strategy</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mf">0.</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">actions</span><span class="p">()}</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-47'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-47'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.344341em;vertical-align:-1.516005em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.808995em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqek" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="mrel mtight">∈</span><span class="mord mathnormal mtight">A</span><span class="mopen mtight">(</span><span class="mord mtight coloredeq eqef" style=""><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.516005em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">535</span>        <span class="n">strategy_sum</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">cum_strategy</span><span class="o">.</span><span class="n">values</span><span class="p">())</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-48'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-48'>#</a>
            </div>
            <p>නම් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.2809409999999999em;vertical-align:-0.29971000000000003em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9722399999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span></span>, </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">537</span>        <span class="k">if</span> <span class="n">strategy_sum</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-49'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-49'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.841882em;vertical-align:-1.170941em;"></span><span class="mord coloredeq eql" style=""><span class="mord" style=""><span class="mord" style="color:cyan"><span class="mord coloredeq eqcf" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqcf" style="">)</span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose coloredeq eqcf" style="">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.670941em;"><span style="top:-2.128769em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mop" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8525400000000001em;"><span style="top:-2.4231360000000004em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7253428571428571em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mop coloredeq eqbd" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9722399999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqbd" style="">(</span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqbd" style="">)</span><span class="mord coloredeq eqbd" style=""><span class="mord" style="color:lightgreen"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:lightgreen">)</span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:lightgreen">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.170941em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">541</span>            <span class="k">return</span> <span class="p">{</span><span class="n">a</span><span class="p">:</span> <span class="n">s</span> <span class="o">/</span> <span class="n">strategy_sum</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">cum_strategy</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-50'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-50'>#</a>
            </div>
            <p>එසේනොමැති නම් </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">543</span>        <span class="k">else</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-51'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-51'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqcl" style=""><span class="mopen" style="">∣</span><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)∣</span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">545</span>            <span class="n">count</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">a</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">cum_strategy</span><span class="p">))</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-52'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-52'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-0.25em;"></span><span class="mord" style="color:cyan"><span class="mord" style=""><span class="mord coloredeq eqcf" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.56778em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">ˉ</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose coloredeq eqcf" style="">)</span><span class="mopen coloredeq eqcf" style="">(</span><span class="mord coloredeq eqcf" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose coloredeq eqcf" style="">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.25744em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqcl" style=""><span class="mopen" style="">∣</span><span class="mord mathnormal" style="">A</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)∣</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqed" style=""><span class="mord" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">548</span>            <span class="k">return</span> <span class="p">{</span><span class="n">a</span><span class="p">:</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">count</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">cum_strategy</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-53'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-53'>#</a>
            </div>
            <p> මානවකියවිය හැකි නිරූපණය</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">550</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-54'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-54'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">554</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-55'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-55'>#</a>
            </div>
            <h2>ප්රතිවිරුද්ධකනගාටුව අවම කිරීම (CFR) ඇල්ගොරිතම</h2>
<p>අපිඅහම්බෙන් නියැදීම් (<strong>සීඑස්</strong>) කරන්නෙමු, එහිදී සියලු අවස්ථා සිදුවීම් (නෝඩ්) නියැදි කර ඇති අතර අනෙක් සියලුම සිදුවීම් (නෝඩ්) ගවේෂණය කරනු ලැබේ. </p>
<p>අපිඅහම්බෙන් නියැදීම් සිදු කරන <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span></span></span></span></span> බැවින් එය සියලු පර්යන්ත ඉතිහාසයන් සඳහා සමාන බැවින් මෙම පදය නොසලකා හැරිය හැකි අතර උපාය ගණනය කිරීමේදී එය අවලංගු වේ (සංඛ්යාංකය සහ නිහාකය තුළ පොදු). </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">557</span><span class="k">class</span> <span class="nc">CFR</span><span class="p">:</span></pre></div>
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    </div>
    <div class='section' id='section-56'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-56'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqcw" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqef" style="margin-right:0.07382em">I</span></span></span></span></span></span></span> සියලු තොරතුරු කට්ටල කට්ටලයක්. </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">570</span>    <span class="n">info_sets</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">InfoSet</span><span class="p">]</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-57'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-57'>#</a>
            </div>
            <ul><li><code  class="highlight"><span></span><span class="n">create_new_history</span></code>
 නව හිස් ඉතිහාසයක් නිර්මාණය කරයි </li>
<li><code  class="highlight"><span></span><span class="n">epochs</span></code>
 මත පුහුණු කිරීමට පුනරාවර්තන සංඛ්යාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqei" style=""><span class="mord mathnormal" style="margin-right:0.13889em">T</span></span></span></span></span></span> </li>
<li><code  class="highlight"><span></span><span class="n">n_players</span></code>
 ක්රීඩකයන් සංඛ්යාව</li></ul>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">572</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span>
<span class="lineno">573</span>                 <span class="n">create_new_history</span><span class="p">:</span> <span class="n">Callable</span><span class="p">[[],</span> <span class="n">History</span><span class="p">],</span>
<span class="lineno">574</span>                 <span class="n">epochs</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
<span class="lineno">575</span>                 <span class="n">n_players</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">2</span><span class="p">):</span></pre></div>
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    </div>
    <div class='section' id='section-58'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-58'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">581</span>        <span class="bp">self</span><span class="o">.</span><span class="n">n_players</span> <span class="o">=</span> <span class="n">n_players</span>
<span class="lineno">582</span>        <span class="bp">self</span><span class="o">.</span><span class="n">epochs</span> <span class="o">=</span> <span class="n">epochs</span>
<span class="lineno">583</span>        <span class="bp">self</span><span class="o">.</span><span class="n">create_new_history</span> <span class="o">=</span> <span class="n">create_new_history</span></pre></div>
        </div>
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    <div class='section' id='section-59'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-59'>#</a>
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            <p>සියලුතොරතුරු කට්ටල <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqcw" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqef" style="margin-right:0.07382em">I</span></span></span></span></span></span></span> කට්ටලයක් සඳහා ශබ්ද කෝෂයක් </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">585</span>        <span class="bp">self</span><span class="o">.</span><span class="n">info_sets</span> <span class="o">=</span> <span class="p">{}</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-60'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-60'>#</a>
            </div>
            <p>විශ්ලේෂණසඳහා ට්රැකර් </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">587</span>        <span class="bp">self</span><span class="o">.</span><span class="n">tracker</span> <span class="o">=</span> <span class="n">InfoSetTracker</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-61'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-61'>#</a>
            </div>
            <p> දීඇති ඉතිහාසයක් සඳහා වර්තමාන ක්රීඩකයාගේ තොරතුරු කට්ටලය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span></span></span> නැවත ලබා දෙයි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">589</span>    <span class="k">def</span> <span class="nf">_get_info_set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">h</span><span class="p">:</span> <span class="n">History</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-62'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-62'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">593</span>        <span class="n">info_set_key</span> <span class="o">=</span> <span class="n">h</span><span class="o">.</span><span class="n">info_set_key</span><span class="p">()</span>
<span class="lineno">594</span>        <span class="k">if</span> <span class="n">info_set_key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">info_sets</span><span class="p">:</span>
<span class="lineno">595</span>            <span class="bp">self</span><span class="o">.</span><span class="n">info_sets</span><span class="p">[</span><span class="n">info_set_key</span><span class="p">]</span> <span class="o">=</span> <span class="n">h</span><span class="o">.</span><span class="n">new_info_set</span><span class="p">()</span>
<span class="lineno">596</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">info_sets</span><span class="p">[</span><span class="n">info_set_key</span><span class="p">]</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-63'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-63'>#</a>
            </div>
            <h3>රුක්ඇවිදින්න</h3>
<p>මෙමකාර්යය ක්රීඩා ගස ඇවිදිනවා. </p>
<ul><li><code  class="highlight"><span></span><span class="n">h</span></code>
 වර්තමාන ඉතිහාසය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span> </li>
<li><code  class="highlight"><span></span><span class="n">i</span></code>
 අපි පරිගණක කනගාටු වන ක්රීඩකයා <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span> වේ </li>
<li><a href="#HistoryProbability"><code  class="highlight"><span></span><span class="n">pi_i</span></code>
</a> වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.2309039999999998em;vertical-align:-0.258664em;"></span><span class="mord coloredeq eqck" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9722399999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span> </li>
</ul><li><a href="#HistoryProbability"><code  class="highlight"><span></span><span class="n">pi_neg_i</span></code>
</a> වේ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.289235em;vertical-align:-0.316995em;"></span><span class="mord coloredeq eqcg" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9722399999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.316995em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span></li>
<p>එයඅපේක්ෂිත උපයෝගීතාව නැවත ලබා දෙයි, ඉතිහාසය සඳහා උපසර්ගය සහිත පර්යන්ත ඉතිහාස සමූහයක් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span> <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.450201em;vertical-align:-1.400196em;"></span><span class="mord coloredeq eqbp" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqeb" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.400196em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqeb" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> කොහේද? <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span></p>
<p>ටීඇවිදින අතරතුර එය සම්පූර්ණ කනගාටුව යාවත්කාලීන කරයි <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord" style="color:orange"><span class="mord" style=""><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span>. </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">598</span>    <span class="k">def</span> <span class="nf">walk_tree</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">h</span><span class="p">:</span> <span class="n">History</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">Player</span><span class="p">,</span> <span class="n">pi_i</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">pi_neg_i</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-64'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-64'>#</a>
            </div>
            <p>එයපර්යන්ත ඉතිහාසයක් නම් පර්යන්ත උපයෝගීතාව <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqdm" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqej" style="margin-right:0.07153em">Z</span></span></span></span></span></span></span> නැවත ලබා දෙන්න <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdq" style=""><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span></span>. </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">619</span>        <span class="k">if</span> <span class="n">h</span><span class="o">.</span><span class="n">is_terminal</span><span class="p">():</span>
<span class="lineno">620</span>            <span class="k">return</span> <span class="n">h</span><span class="o">.</span><span class="n">terminal_utility</span><span class="p">(</span><span class="n">i</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-65'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-65'>#</a>
            </div>
            <p>එයඅහම්බෙන් සිදුවීම් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqdf" style=""><span class="mord" style=""><span class="mord coloredeq eqdu" style=""><span class="mord mathnormal coloredeq eqeh" style="margin-right:0.13889em">P</span></span><span class="mopen coloredeq eqdu" style="">(</span><span class="mord coloredeq eqdu" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose coloredeq eqdu" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqel" style="">c</span></span></span></span></span></span></span> නියැදියක් නම් සහ ඊළඟ පියවරට යන්න. </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">622</span>        <span class="k">elif</span> <span class="n">h</span><span class="o">.</span><span class="n">is_chance</span><span class="p">():</span>
<span class="lineno">623</span>            <span class="n">a</span> <span class="o">=</span> <span class="n">h</span><span class="o">.</span><span class="n">sample_chance</span><span class="p">()</span>
<span class="lineno">624</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">walk_tree</span><span class="p">(</span><span class="n">h</span> <span class="o">+</span> <span class="n">a</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">pi_i</span><span class="p">,</span> <span class="n">pi_neg_i</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-66'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-66'>#</a>
            </div>
            <p>සඳහාවත්මන් ක්රීඩකයාගේ තොරතුරු ලබා ගන්න <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">627</span>        <span class="n">I</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_get_info_set</span><span class="p">(</span><span class="n">h</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-67'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-67'>#</a>
            </div>
            <p>ගබඩාකිරීමට <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.15557em;vertical-align:-0.40557em;"></span><span class="mord coloredeq eqbp" style=""><span class="mop" style=""><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.17862099999999992em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqeb" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.40557em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">629</span>        <span class="n">v</span> <span class="o">=</span> <span class="mi">0</span></pre></div>
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    <div class='section' id='section-68'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-68'>#</a>
            </div>
            <p>එක්එක් ක්රියාව <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.450201em;vertical-align:-1.400196em;"></span><span class="mord coloredeq eqbe" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqeb" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.400196em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mord mtight" style=""><span class="mord mtight" style="">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3567071428571427em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mrel mtight" style="">→</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span> සඳහා ගබඩා කිරීම <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span><span class="mclose">)</span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">633</span>        <span class="n">va</span> <span class="o">=</span> <span class="p">{}</span></pre></div>
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    </div>
    <div class='section' id='section-69'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-69'>#</a>
            </div>
            <p>සියලුක්රියාවන් හරහා නැවත ක්රියා කරන්න </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">636</span>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">I</span><span class="o">.</span><span class="n">actions</span><span class="p">():</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-70'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-70'>#</a>
            </div>
            <p>වත්මන්ක්රීඩකයා නම් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>, </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">638</span>            <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="n">h</span><span class="o">.</span><span class="n">player</span><span class="p">():</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-71'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-71'>#</a>
            </div>
            <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.3644800000000004em;vertical-align:-1.4322400000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9322400000000002em;"><span style="top:-3.93224em;"><span class="pstrut" style="height:3.02224em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.02224em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.02224em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.4322400000000002em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9322400000000002em;"><span style="top:-3.93224em;"><span class="pstrut" style="height:3.02224em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqck" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span><span class="mord coloredeq eqda" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mopen">(</span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.02224em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqcg" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.02224em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.4322400000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">643</span>                <span class="n">va</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">walk_tree</span><span class="p">(</span><span class="n">h</span> <span class="o">+</span> <span class="n">a</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">pi_i</span> <span class="o">*</span> <span class="n">I</span><span class="o">.</span><span class="n">strategy</span><span class="p">[</span><span class="n">a</span><span class="p">],</span> <span class="n">pi_neg_i</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-72'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-72'>#</a>
            </div>
            <p>එසේනොමැති නම් </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">645</span>            <span class="k">else</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-73'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-73'>#</a>
            </div>
            <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.3644800000000004em;vertical-align:-1.4322400000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9322400000000002em;"><span style="top:-3.93224em;"><span class="pstrut" style="height:3.02224em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.02224em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.02224em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.4322400000000002em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9322400000000002em;"><span style="top:-3.93224em;"><span class="pstrut" style="height:3.02224em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqck" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.02224em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqcg" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.02224em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqda" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mopen">(</span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.4322400000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">650</span>                <span class="n">va</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">walk_tree</span><span class="p">(</span><span class="n">h</span> <span class="o">+</span> <span class="n">a</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">pi_i</span><span class="p">,</span> <span class="n">pi_neg_i</span> <span class="o">*</span> <span class="n">I</span><span class="o">.</span><span class="n">strategy</span><span class="p">[</span><span class="n">a</span><span class="p">])</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-74'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-74'>#</a>
            </div>
            <p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.450201em;vertical-align:-1.400196em;"></span><span class="mord coloredeq eqbp" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqeb" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.400196em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.266005em;vertical-align:-1.516005em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.808995em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqek" style=""><span class="mord mathnormal mtight" style="">a</span></span><span class="mrel mtight">∈</span><span class="mord mathnormal mtight">A</span><span class="mopen mtight">(</span><span class="mord mtight coloredeq eqef" style=""><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.516005em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size4">[</span></span><span class="mord coloredeq eqda" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqef" style=""><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span><span class="mclose">)</span><span class="mopen">(</span><span class="mord coloredeq eqek" style=""><span class="mord mathnormal" style="">a</span></span><span class="mclose">)</span><span class="mord coloredeq eqbe" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqeb" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.400196em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mord mtight" style=""><span class="mord mtight" style="">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3567071428571427em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mrel mtight" style="">→</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span><span class="mord"><span class="delimsizing size4">]</span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">655</span>            <span class="n">v</span> <span class="o">=</span> <span class="n">v</span> <span class="o">+</span> <span class="n">I</span><span class="o">.</span><span class="n">strategy</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">*</span> <span class="n">va</span><span class="p">[</span><span class="n">a</span><span class="p">]</span></pre></div>
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    </div>
    <div class='section' id='section-75'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-75'>#</a>
            </div>
            <p>වර්තමානක්රීඩකයා නම් <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>, සමුච්චිත උපාය මාර්ග සහ සම්පූර්ණ කනගාටු යාවත්කාලීන කරන්න </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">659</span>        <span class="k">if</span> <span class="n">h</span><span class="o">.</span><span class="n">player</span><span class="p">()</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span></pre></div>
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    </div>
    <div class='section' id='section-76'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-76'>#</a>
            </div>
            <p>සමුච්චිතඋපාය මාර්ග යාවත්කාලීන කරන්න <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mord coloredeq eqbd" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span><span class="mrel mtight" style="">=</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqed" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord" style="color:lightgreen"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:lightgreen">)</span><span class="mopen" style="color:lightgreen">(</span><span class="mord" style="color:lightgreen"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:lightgreen">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.157819em;vertical-align:-1.329483em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size2">[</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8478869999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdl" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.329483em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span><span class="mclose">)</span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span><span class="mord"><span class="delimsizing size2">]</span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">664</span>            <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">I</span><span class="o">.</span><span class="n">actions</span><span class="p">():</span>
<span class="lineno">665</span>                <span class="n">I</span><span class="o">.</span><span class="n">cumulative_strategy</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">I</span><span class="o">.</span><span class="n">cumulative_strategy</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">pi_i</span> <span class="o">*</span> <span class="n">I</span><span class="o">.</span><span class="n">strategy</span><span class="p">[</span><span class="n">a</span><span class="p">]</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-77'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-77'>#</a>
            </div>
            <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:7.749200999999999em;vertical-align:-3.6246005em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.1246005em;"><span style="top:-7.1093805em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord" style="color:coral"><span class="mord" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8435559999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span><span style="top:-5.2993805em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"></span></span><span style="top:-1.7708485em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord coloredeq eqbt" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqei" style="margin-right:0.13889em">T</span></span><span class="mord" style=""><span class="mord" style="color:orange"><span class="mord coloredeq eqdt" style=""><span class="mord mathnormal" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqei" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span></span><span class="mopen" style="color:orange">(</span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:orange">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord" style="color:orange"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:orange">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.6246005em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.1246005em;"><span style="top:-7.1093805em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="color:pink"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mord" style="color:pink"><span class="mord" style="">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mrel mtight" style="">→</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style="color:pink"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="color:pink">(</span><span class="mord" style="color:pink"><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.843556em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mpunct" style="color:pink">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:pink"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="color:pink">)</span></span></span><span style="top:-5.2993805em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.02224em;"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight coloredeq eqen" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqem" style=""><span class="mord mathnormal" style="">h</span></span><span class="mclose">)</span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord coloredeq eqbe" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqeb" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.400196em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0222399999999998em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqdi" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8703428571428571em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mord mtight" style=""><span class="mord mtight" style="">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3567071428571427em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mrel mtight" style="">→</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqek" style="">a</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbp" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqeb" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.400196em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span><span class="mord"><span class="delimsizing size2">)</span></span></span></span><span style="top:-1.7708485em;"><span class="pstrut" style="height:3.828336em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqep" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mrel mtight">=</span><span class="mord mtight coloredeq eqed" style=""><span class="mord mtight" style="">1</span></span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqei" style=""><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:coral"><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6678599999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord" style="">~</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8435559999999999em;"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mopen" style="color:coral">(</span><span class="mord" style="color:coral"><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mpunct" style="color:coral">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="color:coral"><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="color:coral">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.6246005em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">678</span>            <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">I</span><span class="o">.</span><span class="n">actions</span><span class="p">():</span>
<span class="lineno">679</span>                <span class="n">I</span><span class="o">.</span><span class="n">regret</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+=</span> <span class="n">pi_neg_i</span> <span class="o">*</span> <span class="p">(</span><span class="n">va</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">-</span> <span class="n">v</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-78'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-78'>#</a>
            </div>
            <p>උපායමාර්ගයයාවත්කාලීන කරන්න <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.043556em;vertical-align:-0.25em;"></span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">682</span>            <span class="n">I</span><span class="o">.</span><span class="n">calculate_strategy</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-79'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-79'>#</a>
            </div>
            <p>ක්රීඩකයාසඳහා අපේක්ෂිත උපයෝගීතාව ආපසු ලබා දෙන්න <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq eqen" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>, <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.450201em;vertical-align:-1.400196em;"></span><span class="mord coloredeq eqbp" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.855664em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mrel mtight" style="">∈</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqeb" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqej" style="margin-right:0.07153em">Z</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqem" style="">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op" style="">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.400196em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqdp" style="margin-right:0.03588em">σ</span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqem" style="">h</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span><span class="mord" style=""><span class="mord mathnormal" style="">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqen" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqeq" style="margin-right:0.04398em">z</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span> </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">686</span>        <span class="k">return</span> <span class="n">v</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-80'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-80'>#</a>
            </div>
            <h3>නැවතයාවත්කාලීන කිරීම <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.043556em;vertical-align:-0.25em;"></span><span class="mord" style="color:lightgreen"><span class="mord" style=""><span class="mord coloredeq eqdi" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqdp" style="margin-right:0.03588em">σ</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7935559999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqep" style="">t</span></span></span></span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqef" style="margin-right:0.07847em">I</span></span><span class="mclose" style="">)</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqek" style="">a</span></span><span class="mclose" style="">)</span></span></span></span></span></span></h3>
<p>මෙය <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqei" style=""><span class="mord mathnormal" style="margin-right:0.13889em">T</span></span></span></span></span></span> පුනරාවර්තන සඳහා උපාය මාර්ග යාවත්කාලීන කරයි. </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">688</span>    <span class="k">def</span> <span class="nf">iterate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
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    </div>
    <div class='section' id='section-81'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-81'>#</a>
            </div>
            <p><code  class="highlight"><span></span><span class="n">epochs</span></code>
 වේලාවන් සඳහා ලූප් </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">696</span>        <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">monit</span><span class="o">.</span><span class="n">iterate</span><span class="p">(</span><span class="s1">&#39;Train&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">epochs</span><span class="p">):</span></pre></div>
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    </div>
    <div class='section' id='section-82'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-82'>#</a>
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            <p>ගසඇවිදින්න සහ එක් එක් ක්රීඩකයා සඳහා කනගාටු යාවත්කාලීන කරන්න </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">698</span>            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_players</span><span class="p">):</span>
<span class="lineno">699</span>                <span class="bp">self</span><span class="o">.</span><span class="n">walk_tree</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">create_new_history</span><span class="p">(),</span> <span class="n">cast</span><span class="p">(</span><span class="n">Player</span><span class="p">,</span> <span class="n">i</span><span class="p">),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-83'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-83'>#</a>
            </div>
            <p>විශ්ලේෂණසඳහා දත්ත ලුහුබඳින්න </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">702</span>            <span class="n">tracker</span><span class="o">.</span><span class="n">add_global_step</span><span class="p">()</span>
<span class="lineno">703</span>            <span class="bp">self</span><span class="o">.</span><span class="n">tracker</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">info_sets</span><span class="p">)</span>
<span class="lineno">704</span>            <span class="n">tracker</span><span class="o">.</span><span class="n">save</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-84'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-84'>#</a>
            </div>
            <p>සෑම <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqed" style=""><span class="mord" style="">1</span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">000</span></span></span></span></span> පුනරාවර්තනයක්ම මුරපොලවල් සුරකින්න </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">707</span>            <span class="k">if</span> <span class="p">(</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="mi">1_000</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="lineno">708</span>                <span class="n">experiment</span><span class="o">.</span><span class="n">save_checkpoint</span><span class="p">()</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-85'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-85'>#</a>
            </div>
            <p>තොරතුරුකට්ටල මුද්රණය කරන්න </p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">711</span>        <span class="n">logger</span><span class="o">.</span><span class="n">inspect</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">info_sets</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-86'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-86'>#</a>
            </div>
            <h3>තොරතුරුකට්ටලයක් ට්රැකර්</h3>
<p>තොරතුරුකට්ටල වලින් දත්ත සොයා ගැනීම සඳහා මෙය කුඩා උපකාරක පන්තියකි</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">714</span><span class="k">class</span> <span class="nc">InfoSetTracker</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-87'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-87'>#</a>
            </div>
            <p> සොයාගැනීෙම් දර්ශක</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">720</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-88'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-88'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">724</span>        <span class="n">tracker</span><span class="o">.</span><span class="n">set_histogram</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;strategy.*&#39;</span><span class="p">)</span>
<span class="lineno">725</span>        <span class="n">tracker</span><span class="o">.</span><span class="n">set_histogram</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;average_strategy.*&#39;</span><span class="p">)</span>
<span class="lineno">726</span>        <span class="n">tracker</span><span class="o">.</span><span class="n">set_histogram</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;regret.*&#39;</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-89'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-89'>#</a>
            </div>
            <p> සියලුමතොරතුරු කට්ටල වලින් දත්ත නිරීක්ෂණය කරන්න</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">728</span>    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">info_sets</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">InfoSet</span><span class="p">]):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-90'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-90'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">732</span>        <span class="k">for</span> <span class="n">I</span> <span class="ow">in</span> <span class="n">info_sets</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
<span class="lineno">733</span>            <span class="n">avg_strategy</span> <span class="o">=</span> <span class="n">I</span><span class="o">.</span><span class="n">get_average_strategy</span><span class="p">()</span>
<span class="lineno">734</span>            <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">I</span><span class="o">.</span><span class="n">actions</span><span class="p">():</span>
<span class="lineno">735</span>                <span class="n">tracker</span><span class="o">.</span><span class="n">add</span><span class="p">({</span>
<span class="lineno">736</span>                    <span class="sa">f</span><span class="s1">&#39;strategy.</span><span class="si">{</span><span class="n">I</span><span class="o">.</span><span class="n">key</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">:</span> <span class="n">I</span><span class="o">.</span><span class="n">strategy</span><span class="p">[</span><span class="n">a</span><span class="p">],</span>
<span class="lineno">737</span>                    <span class="sa">f</span><span class="s1">&#39;average_strategy.</span><span class="si">{</span><span class="n">I</span><span class="o">.</span><span class="n">key</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">:</span> <span class="n">avg_strategy</span><span class="p">[</span><span class="n">a</span><span class="p">],</span>
<span class="lineno">738</span>                    <span class="sa">f</span><span class="s1">&#39;regret.</span><span class="si">{</span><span class="n">I</span><span class="o">.</span><span class="n">key</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">:</span> <span class="n">I</span><span class="o">.</span><span class="n">regret</span><span class="p">[</span><span class="n">a</span><span class="p">],</span>
<span class="lineno">739</span>                <span class="p">})</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-91'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-91'>#</a>
            </div>
            <h3>වින්යාසගතකළ හැකි CFR මොඩියුලය</h3>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">742</span><span class="k">class</span> <span class="nc">CFRConfigs</span><span class="p">(</span><span class="n">BaseConfigs</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-92'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-92'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">746</span>    <span class="n">create_new_history</span><span class="p">:</span> <span class="n">Callable</span><span class="p">[[],</span> <span class="n">History</span><span class="p">]</span>
<span class="lineno">747</span>    <span class="n">epochs</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1_00_000</span>
<span class="lineno">748</span>    <span class="n">cfr</span><span class="p">:</span> <span class="n">CFR</span> <span class="o">=</span> <span class="s1">&#39;simple_cfr&#39;</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-93'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-93'>#</a>
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            <p> <strong>CFR</strong> ඇල්ගොරිතම ආරම්භ කරන්න</p>

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            <div class="highlight"><pre><span class="lineno">751</span><span class="nd">@option</span><span class="p">(</span><span class="n">CFRConfigs</span><span class="o">.</span><span class="n">cfr</span><span class="p">)</span>
<span class="lineno">752</span><span class="k">def</span> <span class="nf">simple_cfr</span><span class="p">(</span><span class="n">c</span><span class="p">:</span> <span class="n">CFRConfigs</span><span class="p">):</span></pre></div>
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                <a href='#section-94'>#</a>
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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">756</span>    <span class="k">return</span> <span class="n">CFR</span><span class="p">(</span><span class="n">create_new_history</span><span class="o">=</span><span class="n">c</span><span class="o">.</span><span class="n">create_new_history</span><span class="p">,</span>
<span class="lineno">757</span>               <span class="n">epochs</span><span class="o">=</span><span class="n">c</span><span class="o">.</span><span class="n">epochs</span><span class="p">)</span></pre></div>
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